hii The Transactions of the South African Philosophical Society 
precession. The chief uncertainties lie in the determination of the 
masses of the sun and moon, and their relative mean distances. 
The mass of the sun can be determined by measuring the amount 
which, by its attraction, the sun draws the earth towards itself in a 
second of time. It is an elementary dynamical problem to show that 
the sun’s mass in terms of the earth’s can be expressed in terms of the 
Jength of the seconds pendulum, the number of seconds in the sidereal 
year, the length of the equatorial radius of the earth and the solar 
parallax. The chief uncertainty here, apart from the determination of 
the solar parallax, is the determination of the length of the seconds 
pendulum, which may be 75455 part in error, but that accuracy is 
more than sufficient for our purpose. Therefore, if the solar parallax 
could be determined accurately enough, we should have an exact deter- 
mination of the mass of the sun, and vice versd. 
The distance of the moon is determined with sufficient accuracy by 
direct observations of its parallax ; there remain, therefore, only as data 
for anxious discussion : 
The solar parallax. 
The mass of the moon. 
The precessional moment of inertia. 
The constant of precession. 
The constant of nutation. 
These quantities are correlated by fixed ratios, so that, granted the 
determination of all but one of them, that one becomes known. 
Endless changes have therefore been rung upon these relations. 
Leverrier, in despair of obtaining a determination of the solar parallax 
of sufficient accuracy by any more direct process, attempted to derive it 
from the observed values of the constants of precession and nutation and 
mass of the moon (the latter determined by an independent process 
which will be presently described). Newcomb uses the same process 
as one of several by which he endeavours to arrive at a definitive value 
of the solar parallax. Stone, on the other hand, attempted to determine 
the moon’s mass by assuming—on what basis is not explained—values 
of the sun’s mass and the constants of precession and nutation. In 
fact, the system of deriving values of individual astronomical constants 
from their known relations to each other, without the simultaneous 
consideration of all the correlated quantities, is now admitted to be 
exceedingly unsatisfactory. The one method by which definitive results 
can be reached is to discuss in the first place the value of each constant 
that is capable of determination by strictly independent methods of 
measurement, and to find, from all the reliable independent values of 
‘that constant, its most probable value, and the weight or probable 
error of its determination. Having done this for as many as possible 
